Analysis of Stainless Steel Bipolar Plates Micro-Stamping Processes

Transcription

1 Tsung-Chia CHN, Jiun-Ming Y Deartment of Mechanical ngineering, National Chin-Yi University of Technology, Taichung, Taiwan Analysis of Stainless Steel Biolar Plates Micro-Staming Processes Abstract. Biolar late is one of the key comonents of roton exchange membrane fuel cells (PMFC). Since the roduction costs of traditional grahite biolar lates are very exensive and need a few millimeters thickness over the sace, the resulting metal biolar late not only reduces the cost of such a biolar late, the thickness can also be reduced to micron range. This study aims to exlore the alication of micro-staming technology to roduce thin metal biolar lates with the relevant rocess arameters. Regarding the use of rigid unch on 50μm-thick stainless steel sheet (SUS 304) for micro-channel staming rocess in this study, the channel design is 0.8*0.75mm. Besides, the finite element method and the exerimental results are used to analyze the micro-staming rocess key arameters. In this study, traditional material model and the scale-factor modified material model are used for simulation. The exerimental results verified by the modified material model are more realistic to roducts and have better similarity, as the unch load is relatively small. The results demonstrate that the use of micro-staming roduction of thin metal biolar lates could not only reduce the roduction cost, but could also seed u the rocess. In this aer, using ULF (udated Lagrangian formulation) concet to establish an elastic-lastic deformation finite element analysis model and using scale-factor to modify the calculation could effectively simulate the micro-staming rocess for metal biolar lates. Streszczenie. Dwubiegunowa łyta jest zasadniczym składnikiem baterii PMFC z membranową wymianą rotonową. W artykule zaroonowano zastąienie tradycyjne łyty grafitowej rzez łytę oraz oisano technologię mikro-tłoczenia w celu uzyskania grubości rzędu mikronów. (Analiza rocesu mikrotłoczenia stosowane go do otrzymywania stalowych biolarnych membran o ekstremalnie małych grubościach) Keywords: Micro-staming, Biolar late, Stainless steel, PMFC. Słowa kluczowe: mikrotłoczenie, baterie z wymianą rotonową 1. Introduction Proton exchange membrane fuel cell, as a otential emerging alternative energy, has been widely used in transortation system, cogeneration system, and set-based ower generation system, because of its high efficiency, high ower density, and system stability, etc. [1]-[3]. However, with various comonents of fuel cells, the biolar late is the most imortant, about 60-80% of the stack weight, about 50% of the stack volume, and aroximately 35-45% of stack costs [4]-[6]. For this reason, when the cost of biolar lates is reduced, fuel cells will be widely used. In recent years, many scholars turned to the study on having corrosion-resistant metal biolar lates relaced the grahite biolar lates, mainly because the cost for metal biolar late manufacturing was lower than it for the traditional grahite lates, as well as on the develoment of small forms [7]. Two roblems have shown on current roduction of metal biolar lates. (1) Poor corrosion resistance of metal lates can cause oxidation and decline the erformance of MA. (2) The breakthrough manufacturing technology is lack for the high efficiency, low cost, and high-recision thin metal biolar late rocess [8]. The sheet metal forming rocess has gradually relaced the ast rocessing methods. Regarding sheet metal, staming and hydraulic rocesses are considered the most efficient way to meet the future demand of mass roduction. In revious academic results, the full roof of staming rocess could be effective in thin metal late making a micro-channel, and could serve as an alternative to the roduction of metal biolar lates [9]. Linfa Peng and Peng Hu roosed that micro-staming rocess for biolar lates could imrove roduction efficiency [10]. However, in revious studies, there was no clear indication of the finite element method analysis for microsheet metal staming rocess. Therefore, this aer resented the traditionally macro material stress-strain model and micro scale-factor modified stress-strain model, a different finite element analysis model, to exlore the micro-staming stainless steel sheet rocess. The results showed that the roortion of the thickness scale-factor could effectively simulate the micro sheet metal forming rocess. 2. Basic Theory 2.1. Stiffness quation The equation for virtual work can be made discrete. The udated Lagrangian formulation (ULF) in the alication of an incremental deformation for metal forming rocess (bulk forming and sheet forming) can be ractically alied to describe the incremental roerties of lastic flow. The current configuration, according to the deformation of ULF at each stage, is used as a reference state to evaluate the deformation during a small time interval Δt, such that firstorder theory is consistent with the required accuracy. The rate equation for virtual work, written as an udated Lagrangian equation [11], is (1) ( 2 ) d L L d f v ds ij ik kj ij jk ik ij S i f in which v i is the velocity, ti is the rate of the nominal traction, and and S f reresent the material volume and the surface on which the traction is rescribed. Since the rate equation for the virtual work and the constitutive relation are linear equations of rates, they can be relaced with increments defined with resect to any monotonously increasing measure, such as the increase in the dislacement of the tool. Alying the standard rocedure of finite elements to form the comlete global stiffness matrix, it yields (2) [ K]{ u} { F} in which, (3)[ K T e T ] [ ] ([ ] [ ])[ ] [ ] [ ][ ] B C Q B d Z d In these equations, the term { u} reresents the increment in nodal dislacement and { F} is the rescribed increase in nodal force. [K] reresents the global tangent stiffness matrix; [C e ] is the elemental elastic-lastic constitutive matrix; [B] is the strain rate velocity matrix; and [] is the velocity gradient-velocity matrix. Matrices [Q] and [Z] are defined as stress correction matrices associated with the stress states during each deformation stage.. PRZGLĄD LKTROTCHNICZNY (lectrical Review), ISSN , R. 88 NR 9b/

2 2.2. Selective Reduced Integration Formulation The volume of a lastic medium is incomressible. Therefore, imlementing the full integration technique for finite elements leads to over-strong constraint on thin lates. This henomenon is caused by setting the shear strains γ xz and γ yz to zero during deformation [12]. The selective reduced integration (SRI) rocedure has been roven to effectively treat such roblems as those involving volumetrically stiff contribution [13]. The generalized formulation of SRI, due to Hughes [14], was used to develo the finite element rogram in this study, which used a four-node shell element Scale-Factor for Sheet Metal Micro-Forming Process When the thickness of the sheet metal is larger than 1.0mm, the size effect can be neglected; while the thickness if less than 1.0mm, the size effect then become crucial. For micro-forming rocess the thickness of sheet metals is in micron range that the existed size effect makes traditional material model not suitable for micro-forming rocess. As a result, a new material model needs to be established for micro-staming rocess. al Swift material model (without considering size effect) was first alied in this study. (4) K( 0 ) n The alied sheet metal thickness was 50μm, which was regarded as micro-forming rocess so that size effect should be taken into account. The thickness of sheet metal is taken into traditional material model for stress-strain relations amendment. Consequently, (4) was amended as the follows. dt bt n( ce 1) (5) (, t ) ake ( ) where a, b, c, d are the correction values and t is sheet thickness. The values for a, b, c, d, obtained from the research results of Fang Liu [15], were substituted in (5). Then, t t n(1.0106e 1) (6) ( t, ) Ke ( ) al material model (4) and the modified material model (6) were roceeded finite element analyses in this study. xeriments were further imlemented to verify the differences between the two models. 3. Numerical Analysis This study used quadrilateral four-node shell element to derive the stiffness matrix and CAD software ackage for rocessing model. Due to model symmetry, 1/4 analysis simulation model was adoted to save the comutation time. Sheet metal mesh rocessing was done in the CAD software, converted into data files, and inutted to the 3D elastic-lastic finite element numerical analysis rogram. The analysis of the simulated outut to the CAD software, with further interretation of the software, could show the deformation figures and the distribution of stress and strain. In this study, material roerties, as shown in Table 1, contained the relationshi between equivalent stress and equivalent strain. In the material table, there are two material arameters in macro material model for traditional and modified micro scale-factor model. This study mainly discussed the differences between two material models and the exerimental results as well as observed the deformation of sheet metal biolar lates in micro-staming rocess. The geometric configuration of the tools and the distribution of simulating configuration are shown in Fig. 1, where Rd=0.2mm, R=0.15mm, W=0.80mm, h=0.75mm, and tools ga 60μm. 0 0 Table 1. Mechanical roerties of the SUS304 sheet emloyed in the forming rocess Material (SUS304) (GPa) ν σ y (MPa) K(MPa) n ε Scale-factor The true stress-strain curve is aroximated by K( 0 ) n ; : Young s modulus; v: Poisson s ratio and σ y : yield stress. In this study, L1 section and L2 section were used to measure the thickness and the shae, as shown in Fig. 2. Comarisons of different material models in the microstaming sheet metal rocess were demonstrated. In the simulation, the blank must be added to the aroriate boundary conditions, which must be set in the node. This simulated set of boundary conditions in blank X-axis s nodes had to limit the dislacement in Y-direction and the rotation in Z-direction. In addition, Y-axis s nodes were required to limit the dislacement in X-direction and the rotation in Z-direction. Die Blank Hold Punch A (a) Rigid unch tools Metal Sheet Die Punch (b) Geometries of micro-channel (c) The design of tools (d) Finite element model Fig. 1. Micro-staming rocess to manufacture micro-channel on the stainless steel biolar lates and finite element model. Fig. 2. Measurement diagram Boundary Conditions The contact, or otherwise made by each node, varied with the deformation of the blank. Therefore, during the calculation of the increase in dislacement, the normal comonent of the contacting node force must be checked to determine whether it was less than or equal to zero. The next ste in the calculation of the increase in the dislacement must be changed; that is, the boundary condition of this node became a free node. The free node must also be checked to determine whether it contacted the tool. If so, in the subsequent ste in the calculation of the increase in dislacement, the boundary conditions were changed to those of a contacting node. The above calculation was erformed with an extended r-minimum. 122 PRZGLĄD LKTROTCHNICZNY (lectrical Review), ISSN , R. 88 NR 9b/2012

3 At the contact interface, the discontinuous alternation between the sliding and sticking states of friction occasionally caused comutational difficulty that the treatment of friction conditions required secial attention. A modified Coulomb friction law, roosed by Oden and Pries [16] and Saran and Wagoner [17], was assumed involving two contact friction states, sticking and sliding. This friction law effectively secified the discontinuous variation in the direction of sliding. The simulation of micro-staming rocess conditioned on the assumtion of friction coefficient μ=0.05 to describe the friction condition lastic-plastic Problems The former boundary condition showed that the contact condition remained unaltered within one increment of deformation. Accordingly, the r-minimum method of Yamada et al. [18] was alied and extended to treat elastic-lastic and contact roblems Unloading Problems Sring-back or sring-forward is significant in sheet metal forming. Therefore, the unloading behavior following sheet metal forming was considered. The unloading rocedure was executed, and all elements were reset to be elastic. The force with which the nodes contacted the tools was reversed to become the rescribed force boundary condition on the sheet. (7) f f 4. Results and Discussions Fig. 3 shows the different material models in stainless steel sheet as well as the relationshi between the unch load and the unch stroke. In the calculation rocess, when contacting between sheet and tools, the unch load increased raidly. From the loading simulation, several features were found. In the beginning of formation, the unch load was raidly increased, and the load curve did not resent obvious difference on either traditional or modified material models. Once the unch stroke was increased, the load curve would raidly rise. In the rocess of formation, the curve changes of both models were similar. However, the scale-factor modified material model aeared smaller load curve than the traditional material model did. Load/N Scale factor stroke/mm Fig. 3. The unch load and relative unch stroke for different material model. Fig. 4 shows the geometric deformation of the five stages in the micro-staming rocess for sheet metal biolar lates. Aarently, the sheet metal gradually deformed while staming. Not until the unloading state, were the contact, the searation, and the friction calculated with r-minimum rule in the staming rocess. Stroke=0.00mm Stroke=0.25mm Stroke=0.50mm Stroke=0.75mm After unloading Fig. 4. Micro-staming rocess of the geometric deformation ffect of Material Model In this aer, different material models were used for the analysis of micro-staming rocess, and the differences between the two were exlored. L1 section and L2 section in the simulated and the exerimented sheet metal biolar lates were utilized to measure the thickness and the shae. With comarisons, the feasibility of the modified material model was further verified. Based on the analysis, Fig. 5, the thinnest area aeared on the round corners at both ends of the channel. After comarison, the thinnest area of both models aeared on the modified material model, mm, which merely resented mm difference with the traditional material model. The distribution of the traditional material model was larger than it of the modified material model. With stress distribution, there was stress concentration in the first channel. The reason might be the material flow in the area being more violent. Nonetheless, larger stress aeared on the traditional macro model, 985MPa, which showed 100MPa difference with the modified micro model xeriments of Micro-Staming To rove the roosed henomenon being in accordance with the exerimental roduct, the 50μm-thick stainless steel sheet was receded staming in the traezoid channel. The equiment and the tools for the exeriment are shown in Fig. 6. The exerimental roduct (Fig. 7) was measured the shae with laser dislacement meter. The exerimental results were comared with the simulated results; and, the traditional material model and the scale-factor modified material model were further discussed the differences. PRZGLĄD LKTROTCHNICZNY (lectrical Review), ISSN , R. 88 NR 9b/

4 Thickness (mm) Thickness (mm) (a) Stress (MPa) (b) Stress (MPa) (c) Fig. 5. The results of different material models comare with thickness distribution and stress distribution. (a) al. (b) Modified. (c) al. (d) Modified. (d) (a) Fig. 6. (a) lectronic ress (b) Laser dislacement meter. (b) Fig. 7. The hoto of formed arts of traezoid channel. Fig. 8 dislays the thickness distribution of L1 section (X-axis), where the thickness in the channel was between 0.043~0.033mm. The thinnest area aeared on the to of the channel because of the ull on both sides of the channel. Moreover, the thickest area aeared on the bottom of the transverse channel. The thickness distribution in L1 section did not show large differences between the two material models. However, the least thickness of the roduct and it of the simulation resented obvious differences, after comarison. The error of the thickness distribution on L1 section among the three (traditional material model, modified material model, and exerimental result) was small, within reasonable limits. Furthermore, the thickness distribution on L2 section (Yaxis) was also comared, Fig. 9. The largest thickness error of the three (traditional material model, modified material model, and exerimental result) aeared on the bottom of the middle of channel, with the thickness close to 0.037mm. The thickness distribution outside the channel was about identical. According to the comarison of the 124 PRZGLĄD LKTROTCHNICZNY (lectrical Review), ISSN , R. 88 NR 9b/2012

5 thickness distribution on the two sections among the two material models and the exerimental result, the simulated result of the scale-factor modified material model was close to the exerimental result. However, the errors among the three were within the reasonable 5% (from the asect of engineering) xeriment L1 L1 Channel Height (mm) L1 Thickness (mm) tradition xeriment L X-AXIS (mm) Fig. 10. The shae comarison of L1 section X-Axis (mm) Fig. 8. The thickness distribution of L1 section (X-axis) L2 Channel Height (mm) xeriment L2 Thickness (mm) L L xeriment Y-AXIS (mm) Fig. 9. The thickness distribution of L2 section (Y-axis). Fig. 10 shows the shae comarison of L1 section. Although the differences of the thickness distribution on both material models and the exerimental result were not obvious, there was significant difference on the bottom of the channel. The channel deth of the traditional material model was 0.45mm, and it was about 0.57mm of the scalefactor modified material model that was closer to the exeriment with unload sringback, 0.55mm. Aiming at L2 section, the shae comarison is shown as Fig. 11. The three (traditional material model, modified material model, and exerimental result) resented obvious differences on the bottom of the channel. There was 0.13mm difference between the two models; and, the channel deth of the scale-factor modified material model was closer to the exerimental result. In this case, it was roved that the micro-staming rocess of sheet metal biolar lates could be effectively simulated with finite element analysis and scale-factor modified material model. Y-AXIS (mm) Fig. 11. The shae comarison of L2 section. 5. Conclusions With elastic-lastic finite element analysis and thickness scale-factor modification, the micro-staming rocess for sheet metal biolar lates was studied. In terms of nonlinear management, an increment was alied for calculation; and, with r-minimum to limit the distance between increments, the calculation became linear relation. With the finite element simulation, the following conclusions were obtained. 1. With finite element analysis, the comlete deformation rocess of the sheet metal biolar late micro-staming rocess could be accurately analyzed, meaning that the entire deformation history could be drawn successfully. 2. In micro-forming rocess, the analysis result of the modified material model was closer to the exerimental result. 3. At the round corners on the transverse channel of the biolar late, crackers were likely to aear that the radius of the round corner should be adjusted. The least thickness of the biolar late aeared on the to of the channel that it could be designed as an arc to avoid crackers. 4. Since the tools shae was drawn by CAD software, the develoed finite element analysis model could be PRZGLĄD LKTROTCHNICZNY (lectrical Review), ISSN , R. 88 NR 9b/

6 alied to any other tools shaes for normal microressing rocess. Acknowledgment This aer was suorted by the National Science Council, Taiwan, Reublic of China, through Grant NSC We are grateful to the National Center for High-erformance Comuting for comuter time and facilities. RFRNCS [1] Bar-On I., Kirchain R., Roth R., Technical cost analysis for PM fuel cells, J. Power Sources, 109 (2002), [2] Tawfika H., Hung Y., Mahajan D., Metal biolar lates for PM fuel cell - A review, J. Power Sources, 163 (2007), [3] Hermann A., Chaudhuri T., Sagnol P., Biolar lates for PM fuel cells: A review, Int. J. of Hydrogen nergy, 30 (2005), [4] Li X., Sabir I., Review of biolar lates in PM fuel cells: Flowfield designs, Int. J. of Hydrogen nergy, 30 (2005), [5] Koç M., Mahabunhachai S., Feasibility investigations on a novel micro-manufacturing rocess for fabrication of fuel cell biolar lates: Internal ressure-assisted embossing of microchannels with in-die mechanical bonding, J. Power Sources, 172 (2007), No. 2, [6] Wang S., Peng J., Lui W., Zhang J., Performance of the goldlated titanium biolar lates for the light weight PM fuel cells, J. Power Sources, 162 (2006), [7] Mahabunhachai S., Koç M., Fabrication of micro-channel arrays on thin metallic sheet using internal fluid ressure: Investigations on size effects and develoment of design guidelines, J. Power Sources, 175 (2008), No. 1, [8] Liman T.., dwards J. L., Kammen, D. M., Fuel cell system economics: comaring the costs of generating ower with stationary and motor vehicle PM fuel cell systems, nergy Policy, 32 (2004), [9] Matsuura T., Kato M., Hori M., Study on metallic biolar late for roton exchange membrane fuel cell, J. Power Sources, 161 (2006), [10] Peng L., Hu P., Lai X., Mei D., Ni J., Investigation of micro/meso sheet soft unch staming rocess - simulation and exeriments, Materials and Design, 30 (2009), [11] McMeeking R. M., Rice J. R., Finite element formulations for roblems of large elastic-lastic deformation, Int. J. Solids Structures, 11 (1975), [12] Hinton., Owen, D. R., Finite lement Software for Plates and Shell, Pineridge, Swansea, UK (1984) [13] Hughes T. J. R., The Finite lement Method, Prentice-Hall, nglewood Cliffs, NJ (1987) [14] Hughes T. J. R., Generalization of Selective Integration Procedures to Anisotroic and Nonlinear Media, Int. J. Numerical Methods in ngineering, 15 (1980), [15] Peng L., Liu F., Ni J., Lai X., Size effects in thin sheet metal forming and its elastic-lastic constitutive model, Material and design, 28 (2007), [16] Oden J. T., Pries. B., Nonlocal and nonlinear friction law and variational rinciles for contact roblems in elasticity, J. Alied Mechanics, 50 (1983), [17] Saran M. J., Wagoner R. H., A consistent imlicit formulation for nonlinear finite element modeling with contact and friction: art I theory, Trans. ASM, Journal of Alied Mechanics, 58 (1991), [18] Yamada Y., Yoshimura N., Sakurai T., Plastic Stress Strain Matrix and its Alication for the Solution of lastic-lastic Problems by the Finite lement Method, Int. J. Mech. Sci., 10 (1968), Authors: Tsung-Chia CHN and Jiun-Ming Y are with the Deartment of Mechanical ngineering, National Chin-Yi University of Technology, Taichung, Taiwan. (-mail: ctchen@mail.ncut.edu.tw; bliming.model@gmail.com). 126 PRZGLĄD LKTROTCHNICZNY (lectrical Review), ISSN , R. 88 NR 9b/2012